Title | An Efficient Nominal Unification Algorithm |

Publication Type | Conference Paper |

Year of Publication | 2010 |

Authors | Levy J [1], Villaret M [2] |

Conference Name | Proceedings of the 21st International Conference on Rewriting Techniques and Applications, RTA 2010 |

Conference Location | Edinburgh, Scottland, UK |

Pagination | 209-226 |

ISBN Number | 978-3-939897-18-7 |

Keywords | Higher-Order Unification [3], Nominal Unification [4] |

Abstract | Nominal Unification is an extension of first-order unification where terms can contain binders and unification is performed modulo alpha-equivalence. Here we prove that the existence of nominal unifiers can be decided in quadratic time. First, we linearly-reduce nominal unification problems to a sequence of freshness and equalities between atoms, modulo a permutation, using ideas as Paterson and Wegman for first-order unification. Second, we prove that solvability of these reduced problems may be checked in quadratic time. Finally, we point out how using ideas of Brown and Tarjan for unbalanced merging, we could solve these reduced problems more efficiently. |